Converting the mass ( m ) into energy ( E ) is related to the Einstein relation ( E = mc² ) which is the scientific base of the nuclear bomb where it was found that the fission of the nucleus is associated with losing very small mass and changing into very huge energy as the square of the light velocity is very large quantity ( c² = 9 × 1016 m² / s² ) .

Compton effect

When a photon ( from X or γ rays ) falls on a free electrons , The photon frequency decreases and the photon changes its direction , The electron velocity increases and it changes its direction and this phenomenon is called ” Compton effect ” .

This observation could not be explained by the classical theory of light , but can be explained based on Planck’s hypothesis that electromagnetic radiation consists of photons which can collide with electrons as billiard balls collide ( elastic collision ) .

Sum of the the linear momentum of photon and electron before collision = Sum of the linear momentum of the photon and electron after collision ( law of conversation of linear momentum )

The sum of the energy of photon and electron before collision = The sum of the energy of the photon and electron after collision ( law of conservation of energy )

We find that Compton’s effect proves the particle properties of light , we conclude that the photon moves as a particle which has mass and velocity ( linear momentum ) as well as the electron which proves the particle nature of light , The classical physics could not explain it and it could not be explained except by assuming the existence of photon .

When the photon stops its motion , its mass changes into energy gained by the body which stops it .

It has linear momentum ( PL ) : PL = m c = E / c = h ν / c = h / λ

It has the wave particle duality , So the two conservation laws of mass and energy are applied .

The electron is a particle with a negative charge & has a wave nature , It could be accelerated ( increasing its velocity ) by electric field , it has a linear momentum PL = m v = h / λ , When it stops , it keeps its mass and loses its kinetic energy , It has mass during motion and rest ( me = 9.1 × 10−31 kg ) .

The relation between the wavelength of a photon and its linear momentum

So , The wavelength of a photon equals the ratio between Planck’s constant and the linear momentum of a photon .

The macroscopic and microscopic models of light

When photons fall on a surface , then if the photons wavelength ( λ ) is close to the intermolecular distances , then photons penetrate through atoms and this is what happens in case of X-rays , The microscopic particle model of light is applied in this case .

When photons fall on a surface , then if the photons wavelength ( λ ) is much larger than the intermolecular distances , then photons deals with this surface as a continuous surface and reflect from it ,The macroscopic wave model of light is applied in this case .

So , the macroscopic model and microscopic model are coherent to each other and so , the wave and the particle properties of photons are adjacent also .

Comparison between the microscopic model and macroscopic model for light

The particle model of light ( microscopic ) is applied when an obstacle in the dimensions of atom or electron has obstructed the photons path , It studies the individual photon separately as a ball of radius equals the wavelength of the wave ( λ ) and vibrates in the frequency ( ν ) .

The wave model of light ( macroscopic ) is applied when an obstacle of dimensions much larger than the wavelength of wave has obstructed the photons path , it studies the photons stream as a whole in the form of a wave has a magnetic field and electric field perpendicular to each other and to the direction of their propagation .

Wave properties of a particle

De-Broglie has proved that as waves have a particle nature , particles have a wave nature such that a moving particle is accompanied by a wave its wavelength can be deduced as follows :

λ = c / ν

λ = h / PL

λ = h / m v

De-Broglie equation for particles : The wavelength of a wave accompanying a moving particle equals the ratio between Planck’s constant and the particle’s momentum .

The wave nature of light

The individual photon seems as if carrying the genetic recipes of the wave ( the same properties of photons group ) in terms of frequency , wavelength and velocity .

The wave nature of the electrons

Beam of electrons is enormous group of electrons which has an associated wave that describes its behavior .

The electron seems as if carrying all the genetic recipes ( the same characteristics of the electrons group ) in terms of the mass , the charge , rotation around itself ( lapping spin ) and the linear momentum .

It is clear that we can use an electron ray as we use light ray , This is the base of the electron microscope .

Electron microscope and optical microscope

The electron microscope

To form an enlarged image of small objects , it is necessary that the wavelength of the used wave in photography to be less than the dimensions of the body to be configured and the wavelength of the normal light has a limited dimensions , so the optical microscope can not be used to see very small objects such as viruses .

The wave nature of the electron

We can calculate the wavelength of the wave which is associating the motion of the electron by using De-Broglie equation : λ = h / m v

So , by increasing the potential difference between the cathode and anode in the electron microscope its kinetic energy increases the velocity of the electron ( v ) increases , the wavelength ( λ ) of the wave which is associating the electron decreases until it becomes less than the dimension of the body , so a magnified image is formed .

Optical microscope: The used beam is light beam , The used lenses are glass lenses to concentrate the light on the body to magnify it , resolving power is low , magnification power is limited as it fails to distinguish the fine details .

Electron microscope : The used beam is electron beam with wavelength shorter than the wavelength of the light beam by 1000 times , The used lenses are electronic ( magnetic ) lenses to focus the electron beam on the body to magnify it , resolving power is high as the electron can carry high kinetic energy and hence very short wavelength ( λ ) , so it can detect very small objects that the normal light fails to observe , magnification power is very high , so it can distinguish the fine details .